Differentiability with Respect to Initial Data for a Scalar Conservation Law

  • François Bouchut
  • François James
Part of the International Series of Numerical Mathematics book series (ISNM, volume 129)


We linearize a scalar conservation law around an entropy initial datum. The resulting equation is a linear conservation law with discontinuous coefficient, solved in the context of duality solutions, for which existence and uniqueness hold. We interpret these solutions as weak derivatives with respect to the initial data for the nonlinear equation.


Initial Data Cauchy Problem Entropy Solution Duality Solution Weak Stability 
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Copyright information

© Springer Basel AG 1999

Authors and Affiliations

  • François Bouchut
    • 1
    • 2
  • François James
    • 1
    • 2
  1. 1.Mathématiques, Applications et Physique Mathématique d’OrléansUMR CNRSFrance
  2. 2.Université d’OrléansOrléans Cedex 2France

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